Intervals on weakly ordered partial commutative groups of
linear operators

D 2012

Intervals on weakly ordered partial commutative groups of linear operators

JANDA, Jiří

Základní údaje

Originální název

Intervals on weakly ordered partial commutative groups of linear operators

Autoři

JANDA, Jiří (203 Česká republika, garant, domácí)

Vydání

Shaanxi Normal University, China, Quantitative Logic and Soft Computing: Proceedings of the QL&SC 2012, Xian, China 12-15 May 2012, od s. 693-701, 9 s. 2012

Nakladatel

World Scientific Publishing Company, 2012

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10101 Pure mathematics

Stát vydavatele

Čína

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Kód RIV

RIV/00216224:14310/12:00067542

Organizační jednotka

Přírodovědecká fakulta

ISBN

981-4401-52-8

UT WoS

000343469800091

Klíčová slova anglicky

(generalized) effect algebra; weakly ordered partial group; Hilbert space; unbounded linear operator; states; interval effect algebra

Štítky

AKR, rivok

Změněno: 4. 4. 2013 14:07, Mgr. Jiří Janda, Ph.D.

Anotace

V originále

The generalized effect algebra was presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on Hilbert space with the usual sum of operators. A structure of the set of not only positive linear operators can be described with the notion of weakly ordered partial commutative group (wop-group). With a restriction of the usual sum, the important subset of all self-adjoint operators forms a substructure of the set of all linear operators. We investigate the properties of intervals in wop-groups of linear operators and showing that they can be organised into effect algebras with nonempty set of states.

Návaznosti

EE2.3.20.0051, projekt VaV

Název: Algebraické metody v kvantové logice

MSM0021622409, záměr

Název: Matematické struktury a jejich fyzikální aplikace

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Matematické struktury a jejich fyzikální aplikace

Citovat

JANDA, Jiří. Intervals on weakly ordered partial commutative groups of linear operators. In Guojun Wang, Bin Zhao, Yongming Li. Quantitative Logic and Soft Computing: Proceedings of the QL&SC 2012, Xian, China 12-15 May 2012. Shaanxi Normal University, China: World Scientific Publishing Company, 2012, 2012, s. 693-701. ISBN 981-4401-52-8.

@inproceedings{1075231,
   author = {Janda, Jiří},
   address = {Shaanxi Normal University, China},
   booktitle = {Quantitative Logic and Soft Computing: Proceedings of the QL&SC 2012, Xian, China 12-15 May 2012},
   editor = {Guojun Wang, Bin Zhao, Yongming Li},
   keywords = {(generalized) effect algebra; weakly ordered partial group; Hilbert space; unbounded linear operator; states; interval effect algebra},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Shaanxi Normal University, China},
   isbn = {981-4401-52-8},
   pages = {693-701},
   publisher = {World Scientific Publishing Company, 2012},
   title = {Intervals on weakly ordered partial commutative groups of linear operators},
   year = {2012}
}

TY  - CONF
ID  - 1075231
AU  - Janda, Jiří
PY  - 2012
TI  - Intervals on weakly ordered partial commutative groups of linear operators
PB  - World Scientific Publishing Company, 2012
CY  - Shaanxi Normal University, China
SN  - 9814401528
KW  - (generalized) effect algebra
KW  - weakly ordered partial group
KW  - Hilbert space
KW  - unbounded linear operator
KW  - states
KW  - interval effect algebra
N2  - The generalized effect algebra was presented as a generalization of effect algebra for an algebraic description of the structure of the set of all positive linear operators densely defined on Hilbert space with the usual sum of operators. A structure of the set of not only positive linear operators can be described with the notion of weakly ordered partial commutative group (wop-group). With a restriction of the usual sum, the important subset of all self-adjoint operators forms a substructure of the set of all linear operators. We investigate the properties of intervals in wop-groups of linear operators and showing that they can be organised into effect algebras with nonempty set of states.
ER  -

JANDA, Jiří. Intervals on weakly ordered partial commutative groups of linear operators. In Guojun Wang, Bin Zhao, Yongming Li. \textit{Quantitative Logic and Soft Computing: Proceedings of the QL\&{}SC 2012, Xian, China 12-15 May 2012}. Shaanxi Normal University, China: World Scientific Publishing Company, 2012, 2012, s.~693-701. ISBN~981-4401-52-8.

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